Asymptotic Behavior Of Third Order Nonlinear Difference Equations With Mixed Arguments - Arul, R. (JOURNAL OF ADVANCES IN MATHEMATICS, 2014)
In this paper, we established criteria for asymptotic properties of nonlinear dierence equation with mixed arguments of the form ? 2(an(? xn)a) + qnf(xn-l) + pnh(xn+m) = 0, n ? N 0 where an, pn and qn are nonnegative real sequences, a is a ratio of odd positive integer, and l and m are positive integers. We duduce the properties of studied equation by establishing new comparison theorem, so that some asymptotic properties of nonoscillatory solutions are resulted from the oscillation of a set of first order difference equations. Some examples are provided to illustrate the main results.